The White House on Thursday invited the leaders of the House and Senate intelligence committees to view U.S. spy documents related to accusations of Obama administration surveillance of Trump campaign officials as Russian experts on Capitol Hill outlined tactics used by Moscow to spread “fake news” and influence U.S. policy.

White House Press Secretary Sean Spicer declined to specify what was in the documents, but he stressed that President Trump remained convinced that his campaign was improperly targeted for surveillance by the Obama administration.

“We want to make sure the people conducting the investigation have access to it,” he said.

The invitation went out to the top Republican and Democrat on the committees amid a news report that White House officials provided similar documents to Rep. Devin Nunes, California Republican and chairman of the House Intelligence Committee.

While the information, according to the letter, related to President Trump and his associates being swept up in surveillance activities, the committees also are probing Russian meddling in the election and possible Trump campaign collusion with the Kremlin.

Rep. Adam B. Schiff of California, the ranking Democrat on the House Intelligence Committee, said that he had accepted the invitation but vowed not to be diverted from the Russian probe.

“This issue is not going to distract [us] from doing our Russia investigation,” Mr. Schiff told reporters at the Capitol. “We are not going to be deterred.”

Mr. Schiff has spearheaded the probe into accusations that Mr. Trump and his associates conspired with Russian spies to undermine the campaign of Democratic presidential nominee Hillary Clinton.

U.S. intelligence agencies determined that Russia was behind email hacks and other activities that hurt Mrs. Clinton’s campaign. No evidence of Trump campaign involvement has been produced.

Mr. Nunes was harshly criticized by Mr. Schiff and others last week when he announced that he had received documents showing Mr. Trump and his associates were caught in surveillance of Russian spies and their identities “unmasked” in intelligence reports, a possible violation of federal privacy laws.

They questioned the source of the documents and faulted Mr. Nunes for briefing Mr. Trump on the material before committee members. He was accused of acting as a surrogate for the White House and impugning the credibility of the investigation.

Mr. Schiff and others called on Mr. Nunes to remove himself from the investigation or step down as chairman, demands he has refused with the backing of both Mr. Trump and House Speaker Paul D. Ryan.

It was unclear if the documents the White House invited lawmakers to view were the same documents examined by Mr. Nunes.

The intrigue surrounding the source of the documents deepened with a New York Times report that implicated two White House officials.

Citing several U.S. officials, the newspaper reported that Ezra Cohen-Watnick, the senior director for intelligence at the National Security Council, and Michael Ellis, a lawyer who works on national security issues at the White House Counsel’s Office, helped supply Mr. Nunes with the spy documents.

Mr. Ellis formerly worked on the staff of the House Intelligence Committee.

On Capitol Hill, Sen. Richard Burr, Republican chairman of the Senate Intelligence Committee, opened the Senate’s first hearings on Russia by vowing to find the truth and predicting it will take months — if not longer — to complete the probe of Moscow’s activities.

“How they came to be involved, how we may have failed to prevent that involvement, what actions were taken in response, if any, and what we plan to do to ensure the integrity of future, free elections at the heart of our democracy” will all be on the table, said Mr. Burr of North Carolina.

His comments were buttressed by similar statements from ranking Intelligence Committee Democrat Mark R. Warner in a calculated move by the Senate to try and inject a modicum of sobriety into an investigation that has found itself at the center of a media firestorm over the extent to which Mr. Trump or any of his associates may have known of Russia’s meddling prior to the 2016 election.

For a second day in a row, Mr. Burr and Mr. Warner of Virginia sought to tamp down partisan backbiting over Mr. Nunes that has stunted a parallel House side probe.

Mr. Burr said the committee’s investigation “will fail” if members allow politics to get in the way, and has put his weight behind a plan by the Senate to question 20 people, including Mr. Trump’s son-in-law and adviser, Jared Kushner.

It is not yet clear when Mr. Kushner will testify. But lawmakers inquired after his meeting Russia’s ambassador to Washington in December, and also with the head of Russia’s state-owned development bank.

Administration supporters say those meetings were normal engagements for an adviser to a leading presidential campaign, but critics claim they could be the tip of a conspiracy between the Trump team and Moscow.

Thursday’s hearings had a less focused tenor, with testimony from a collection of cybersecurity and Russian history experts, as well as retired Army Gen. Keith Alexander, who served until 2014 as director of the National Security Agency and as the first chief of U.S. Cyber Command.

Roy Godson, a Georgetown University professor and longtime national security consultant, told the panel that Russian meddling is occurring not just in the U.S., but around the world — and that President Vladimir Putin has sought to foster in an era of clandestine subversion akin to what the Soviet Union engaged in at the height of its power a half-century ago.

Mr. Putin, whose own background is in the Soviet KGB, came to the fore in 1999 with “a coterie of former colleagues, many also trained in the Soviet security and intelligence system,” Mr. Godson said, adding the group is bent on “discrediting the U.S. and democratic society in general.”

“Their focus is almost completely negative, zeroing in on creating chaos and division in what has been called an ‘age of anger’ in many parts of the world,” he said. “This opens up many opportunities for influence.”

Mr. Alexander told lawmakers Russia’s international subversion operations date back to the 1920s, and noted how onetime KGB Maj. Gen. Oleg Kalugin described them as “the heart and soul of the Soviet intelligence,” specifically designed to “weaken the West, to drive wedges in the Western community alliances of all sorts, particularly NATO [and] to sow discord among allies.”

There were a few unexpected revelations in the more than four hours of testimony from the historians, cyberexperts and former intelligence officials.

Sen. Marco Rubio, Florida Republican, told his colleagues on the committee that in the previous 24 hours, his former presidential campaign team was unsuccessfully targeted — for the second time — by hackers at an unknown internet address in Russia. Mr. Ryan also was targeted by internet hackers recently, said Clint Watts of the Foreign Policy Research Institute.

Eugene Rumer from the Carnegie Endowment for International Peace said the Russian work is not always conducted in the shadows.

“They hacked 3,000 to 4,000 people. This hacking was pervasive,” he said, lamenting how the American people have focused too much on the election season hack of the Democratic National Committee. “They have our information,” and could use it later for political purposes.

As the hearing got underway in Washington, Mr. Putin dismissed the accusations as “endless and groundless,” telling reporters in Moscow that they are part of a U.S. domestic political struggle.

“This anti-Russian card is being played in the interests of some political forces inside the United States with an aim to strengthen and consolidate their positions,” he said, without naming anyone.

In Washington, Democrats’ calls for Mr. Nunes to step down from the investigation intensified.

Mr. Schiff said that The New York Times report, if accurate, raised “profound questions” about how the White House was using Mr. Nunes and why the source of the material was being hidden.